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C 2011 American Chemical Society

Thermionic Field Emission Transportin Carbon Nanotube TransistorsDavid J. Perello,† Seong Chu Lim,‡ Seung Jin Chae,‡ Innam Lee,† Moon. J. Kim,§ Young Hee Lee,‡,* and

Minhee Yun†,*

†Department of Electrical Engineering, University of Pittsburgh, Pittsburgh Pennsylvania 15219, United States, ‡Department of Physics, Department of EnergyScience, Sungkyunkwan Advanced Institute of Nanotechnology, Suwon 440-746, Republic of Korea, and §Department of Materials Science and Engineering,University of Texas - Dallas, Richardson, Texas 75080, United States

Current modulation in carbon nano-tube field effect transistors (CNTF-ETs) is dominated by field-adjusted

energy barriers at the contacts,1-5 in con-trast to Si-based devices.6 Without chemicaltreatment, the metal-contact work functiondetermines the CNT device polarity,7,8 ap-plicable in advanced adaptive logic circuits9

and dopant-free complementary metal-oxide semiconductor (CMOS) circuitry.10-12

However, previous attempts at understand-ing the contact physics of CNTFETs13-16 arecomplicated by the usage of CNT withvarying diameter and the lack of an analy-tical CNT transport model. Therefore, herewe report systematic experimental and the-oretical analysis relatingmetal-contact workfunction and electrical transport propertiessaturation current (Isat) and differential con-ductance (σsd) in CNTFETs, incorporating atheoretical model analytically derived fromthermionic field emission. Previous limita-tions are overcome with measurement, sta-tistical analysis, and data fitting from ∼100Hf, Cr, Ti, Au, and Pd contacts on a singleCNT. Further analysis suggests the model isapplicable for quantitative nanotube-basedgas sensing and for noninvasive metalwork-function measurement.

RESULTS

CNTFETs are fabricated using e-beamlithography and physical evaporation ontocentimeter long, aligned, laminar flowgrown thermal chemical vapor deposition(CVD) CNTs.17 Metal contacts were placed ina linear fashion along the tube length withan equidistance of 1 μm gap (Figure 1a).After fabrication, additional CNTs on thesample were removed with 100-150 W O2

plasma, while areas containing FETs werecovered with protective sacrificial layer ofphoto resist. This resist was removed, andthe samplewas cleaned twicebyUVexposure

and further rinsed in acetone to remove anyresidue. Atomic force microscopy (AFM)measurements confirmed the cleanlinessof the sample. We focus on two samples inthis report, the first contains 120 electrodes(114 devices) on a single 6 mm long semi-conducting CNT of 1.7 nm diameter with86 devices electrically active at the firstmeasurement (75.4% yield). The diameterwas confirmed by AFM, and the lack of100% yield results from regions where thesingle CNTwas damaged during fabrication.Sample 1 utilizes themetals Ti, Pd, Cr, andHfasmetal contacts. In addition, to confirm themodel consistency, we prepared a secondsample incorporating only Ti and Au elec-trodes on a 5 mm long, 1.53 nm diametersemiconducting CNT. Optical images of sam-ples are shown in Figure 1a and a magnifiedAFM image in Figure 1b. Themetals Au, Ti, Pd,Cr, and Hf were chosen because they arenonferromagnetic and possess a wide rangeof work functions (4.0-5.2 eV).

CHARACTERIZATIONANDDISCUSSION

I-V measurements were performed onthe two samples in ambient environment

* Address correspondence toleeyoung@skku.edu,miy16@pitt.edu.

Received for review September 8, 2010and accepted January 27, 2011.

Published online10.1021/nn102343k

ABSTRACT With experimental and analytical analysis, we demonstrate a relationship between

the metal contact work function and the electrical transport properties saturation current (Isat) and

differential conductance (σsd = ∂Isd/∂Vsd) in ambient exposed carbon nanotubes (CNT). A single

chemical vapor deposition (CVD) grown 6 mm long semiconducting single-walled CNT is electrically

contacted with a statistically significant number of Hf, Cr, Ti, Pd, and Au electrodes, respectively. The

observed exponentially increasing relationship of Isat and σsd with metal contact work function is

explained by a theoretical model derived from thermionic field emission. Statistical analysis and

spread of the data suggest that the conduction variability in same CNT devices results from

differences in local surface potential of the metal contact. Based on the theoretical model and

methodology, an improved CNT-based gas sensing device layout is suggested. A method to

experimentally determine gas-induced work function changes in metals is also examined.

KEYWORDS: carbon nanotube . thermionic field emission . schottky barrier .electrical transport . saturation current . differential conductance

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using a probe station. A back gate bias of Vg = -15 Vwas found to be sufficient to bias all devices in the hole-conducting on-state. This restriction was necessary toprevent the existence of multiple carrier types andeliminate the effect of threshold voltage shifts in theanalysis of different metals. Figure 1c shows the clearIsd relationship withmetals, with an order of I(Hf) < I(Cr)< I(Ti) < I(Pd). Isat is found by extrapolating the linearregion of ln(Isd) vs Vsd to Vsd = 0 V, as illustrated inFigure 1c. The corresponding σsd curves are alsoprovided in Figure 1d. To calculate σsd, Isd(Vsd) curveswere smoothed with a 16 point Savitzky Golay filter,and the resulting curves are differentiated. The datawere tabulated by metal type, and differential con-ductance at Vsd = 0 point was chosen from each devicefor comparison.To accurately compare σsd and Isat for differentmetal

contacts, statistical analysis is performed on the rawdata to check the normality of each distribution. Fordata with a normal distribution, the mean will be usedas an accurate comparative value to test for a depen-dence between metal σsd and Isat. Figure 2a shows ahistogram of differential conductance by metal type.Although there is an overlap in the differential conduc-tance for eachmetal, a distinct trend for σsd is observedwith an order, σsd(HF) < σsd (Cr) < σsd (Ti) < σsd (Pd). Itwill be demonstrated later in this report that the overlapis attributable to the widely varying and often over-lapping work functions for each of the metal species. AShapiro-Wilk normal distribution test of the data withR = 0.05 permitted rejection of the normal distributionhypothesis for the metal Pd due to the wide asym-metric distribution of the data.18 In this case, σsd for Pd-contacted devices is very unlikely to be representative

of a normal distribution, as expected due to the ohmicqualities of many devices limiting the upper range ofconductance. To examine the dependence ofmean σsdon work function of Hf, Cr, Ti, and Au metal, ln(σsd) vswork function (see Table S1, Supporting Information,for more details) is plotted in Figure 2b. A linearrelationship between ln(σsd) and work function isobserved, although nonlinearity comes into play atlarge work function.In order to understand the relationship between

ln(σsd) and work function, we begin with TFE current,since strict thermionic emission current and field emis-sion current will give rise to a linear relationship. Purethermionic emission theory also predicts that ln(σsd)�(Φmetal)/(kT) = 38.61 (see data S1, SupportingInformation). A simple linear fit of the data producesa slope <10, indicating the presence of a large fieldemission component. Therefore, a mixed TFE theoryadopted from Crowell et al.19 and Padovani et al.20 isincorporated to fit the experimental observations. TFEcurrent at a metal-semiconductor junction is de-scribed by

Isd ¼ Isat[eVsd=kT - 1] (1)

with

Isat ¼ Aπ1=2E001=2(Φb - Vsd þ ς2)

1=2

kTcoshE00kT

� � � e(ς2kT -

Φb þ ς2E0

)(2)

where A is the Richardson constant, T is temperature inKelvin, k is the Boltzmann constant,Φb is the Schottkybarrier height, ζ2 = EF- EV, EF is the CNT Fermi level, EVis the CNT valence band, E00 is a TFE tunneling param-eter,19 and E0 = E00coth(E00/kT). Applying Vg = -15 V

Figure 1. Device structure and electrical properties of SWCNT. (a) Optical and (b) AFM images of CNTFET devices. Scale bar is1 mm for optical and 20 μm for AFM image. (c) Isd vs Vsd curves for a group of metals on the same CNT. Example ofextrapolation procedure used to estimate Isat is shown in the case of a Ti contact. (d) Differential conductance curves forsample of Hf, Cr, Ti, and Pd metals exemplifying metal dependence.

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results in ζ2 = EF - EV ≈ 0, simplifying the system. Weutilize the Schottky-Mott relationship and assumethat Φb ≈ Φs- Φm. From the value of graphite,electron affinity, XCNT ≈ 4.5, and for a CNT diameterof 1.7 nm, energy gap, Eg ≈ 0.65 eV.21 Therefore,Φb ≈5.15 - Φm, allowing replacement of the barrier de-pendence with a work function dependence. Furtherdifferentiating eq 1 and substituting eq 2 with theabove relationships forΦb, we derive (refer to data S2,Supporting Information for full derivation):

ln(σsd)�12ln(5:15-Φm)-

1E0

� �(5:15-Φm) (3)

The fitting of this function to Hf, Cr, Ti, and Au isshown in Figure 2b. These results allow extraction oftunneling parameters E0 = 0.147 eV = E00 and kT/E00 ≈0.176. The analysis of Crowell and Rideout is next usedto find RM = Ecarriers/Φb = cosh(E00/kT)

-2,19 where RM isdefined as a ratio of carrier energy Ecarriers to barrierheight Φb; RM ≈ 0 from our model, indicating thatmost carriers tunnel directly to the valence bandmaximum. As a result of assumptions in the derivation,the excellent fit of eq 3 to the experimental observa-tions strongly supports the existence of an unpinnedFermi level at metal-CNT interface. The source of thenonlinearity in Figure 2b results from growth of thelogarithmic term in eq 3 as Φm w 5.15. Phenomen-ologically, the energy barrier is sufficiently small andthe field emission dominant such that variations inbarrier height produce little to no change in differentialconductance.We next consider the saturation current of the above

measured Schottky field effect transistors (SFETs) as afunction of metal work function to further validate thetheoretical model and the accurate fitting of thedifferential conductance. Isat for the metals was foundby using both ( Vsd curves from all device measure-ments, as the positive and negative voltage regimesare correlated to the source/drain contacts separately(hence two Isat values for each device).

22 A histogramof

the raw data is shown in Figure 3a. The Shapiro-Wilknormal distribution test of these data again allowedrejection of the possibility that Pd came from a normaldistribution for R = 0.05. The data set for the saturationcurrent is significantly larger than that for differentialconductance due to the use of both ( Vsd from rawdata, hence (other than Pd) the distributions havemore visually symmetrical shape.Interestingly, the exact same TFE relationship as for

σsd can be used to fit Isat, using equivalent workfunction and Fermi level assumptions (see data S3,Supporting Information). Pd was not included in thefitting, again because the sample mean was not re-flective of the asymmetric distribution. Figure 3bshows ln(Isat) vs work function. The extracted tunnelingparameters, E0 = 0.139 = E00 and kT/E00 ≈ 0.186, aresimilar to those of differential conductance. This in-dicates that TFE and the derived model explain holeconduction in CNTFETs accurately.Next, we consider the small variation of differential

conductance (and Isat) observed particularly in the caseof Au and Cr in Figure 2. These metals are in contrastwith Pd and Hf in which a large variation was observed.Further, if one fits the raw data variance onto theobserved curve of ln(σsd) vs Φb, the resulting workfunction spread falls within the expectedwork functionrange observed in ambient, indicating strong correla-tion between local work function and σsd. This phe-nomenon is demonstrated in Figure S1, SupportingInformation. It is therefore concluded that variation ofσsd (and Isat) is strongly related to environmentalstability of metal, since the work function can be easilymodified by adsorbates (particularly in the case of Pdand Hf). Implication of our measurements and theore-tical model fitting is very intriguing, particularly for gassensing. Physisorption of gases on a metal alters thework function and surface dipole according to expo-sure dose, often bywell-known relationships. While themetals display no change of conductance with expo-sure, when used as a contact to a CNT, the work

Figure 2. Raw data of differential conductance (σsd) and fitting to theoretical thermionc field emissionmodel. (a) Histogramsof ln(σsd) at Vg =-15 V. In order of smallest to largest mean value: Hf, Cr, Ti, Au, Pd; (b) ln(σsd) plotted vs contact metal workfunction. The differential conductance value used for fitting each metal is the mean of the distributions in (a). Work functionrange is from the literature (T1, Supporting Information). Hf and Pd arrows are due to the possibility of large work functionvariations; in these cases the theoretical or only available literature values were chosen.

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function and dipole change will result in a measurableIsat and σsd difference explainable by the relationshipsderived in this report.An initial constraint to this sensing approach is the

variation in conducting properties for different CNTunder varying initial environmental conditions. How-ever, the use of different diameter CNT will only affectCNT work function, and a simulation of curves in-creased (decreased) saturation current for smaller(larger) diameter CNT is seen in Figure 4. Similar trendsare visible for each diameter, but the model fails at alower metal contact work function due to the smaller

CNT work function in larger diameter tubes. In CNTwith a diameter 3.0 nm, Isat approaches 15 μA, similar towhat has been observed experimentally. This suggeststhat with large work function metal contacts, themodel can also predict Isat in other CNT devices.23

Therefore, simple I-V measurement during exposurewill allow extraction of the work function of the metal,which will in turn allow one to measure the existenceand even the concentration of certain gas species,which previously has been impossible to quantify.

CONCLUSION

In conclusion, we have demonstrated clear workfunction-dependent relationships for hole current σsdand Isat. These parameters have been correlated by anexisting contact-dominant conduction mechanism.Using TFE theory, tunneling parameterswere extractedusing a novel characterization method that stronglysuggests an unpinned Fermi level in carbon nano-tubes. Additionally, the results for σsd and Isat fittingsare in agreement, and the mathematical model pre-sented can also be utilized to selectivity sense adsor-bates in single CNT sensors via contact work functionchange. The process could further be reversed todetect work function of a metal in the case of a well-controlled environment, an important discovery formaterials where local probing or optical methods areimpossible.

METHODSFabrication. CNTs were synthesized by thermal CVD with

FeCl3 (Sigma Aldrich) in ethanol as a catalyst using flow ratesof 16 sccm H2, 8 sccm CH4, and 100 sccm Ar in a 50 mm quartztube. To contact the CNT with multiple metal species, mod-ular Ti/Au probe-able pads were first fabricated with leadlines within∼15 μmof the CNT; via e-beam lithography (RaitheLine) and e-beam evaporation. Sequentially, Pd, Cr, Hf, and Tielectrodes were patterned with e-beam lithography, metaldeposition performed by e-beam evaporation, and lift-off carried

out in warm acetone. Post fabrication, CNTFET regions werecovered with protective photoresist, and the samples werecleaned in 150 W O2 plasma to remove unused CNTs.

Characterization. I-V curves were measured using a Keithley236 (Source/Drain) and Keithley 237 (Gate/Drain) with Labviewinterface. Data analysis was performed using plotting softwareOrigin 8.0 (Origin Laboratories).

Acknowledgment. The Pittsburgh group would like to ac-knowledge the Air Force Office of Scientific Research through a

Figure 3. Raw data of ln(Isat) and fitting to theoretical thermionic field emissionmodel. (a) Raw data of ln(Isat) at Vg =-15 as afunction of metal. (b) Fitting of themean values of ln(Isat) for Hf, Cr, and Ti to TFEmodel derived and discussed in the text. Theerror bounds for work function are taken from the literature (Table S1, Supporting Information). Hf and Pd arrows are due topossibility of large work function variations; in these cases the theoretical or only available literature values were chosen.

Figure 4. Simulation of diameter effect on ln(Isat) best fitcurves. Simulated ln(Isat) curves for different diameter CNTusing the model and constants from the text, assumingE00 = 0.147 and that all other factors except CNT workfunction are constant.

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grant provided by MEST and NSF ECCS 1039543. The SKKUgroup would like to thank KICOS through a grant provided byMOST in 2007 (no. 2007-00202) and in part the Ministry ofEducation through the STAR-faculty project, TND Project, andthe KOSEF through CNNC at SKKU.

Supporting Information Available: Derivation of limitingthermionic conditions and of eq 3 for σsd and Isat, correlationof data spread for σsd and work function, and literature workfunctions. This information is available free of charge via theInternet at http://pubs.acs.org.

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